Time Value of Money
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| Future Value - formula, definition | FV = P x 〖(1+r)〗^t
Future Value - Amount to which an investment will grow after earning interest.
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| Distinguish between simple & compound interest | Compound Interest - Interest earned on interest.
Simple Interest - Interest earned only on the original investment; no interest is earned on interest.
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| Present Value | PV = (FV or C)/ (1 + r)^t
= future value (or cash flows) over (1+ discount rate) to the power of t.
Present Value - Value today of a future cash flow.
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| Distinguish between discount factor and discount rate. | Discount Factor - Present value of a $1 future payment.
Discount Rate - Interest rate used to compute present values of future cash flows
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| Time Value of Money (applications) | Value of Free Credit
Implied Interest Rates
Internal Rate of Return
Time necessary to accumulate funds
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| Perpetuities | Perpetuity - A stream of level cash payments that never ends. e.g., consols
PV of perpetuity = c/r
C = cash payment
R = interest rate
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| Annuities | Annuity - Equally spaced level stream of cash flows for a limited period of time. e.g., mortgage, car loan
PV of t year’s annuity =
C [ (1/r) - (1/(r (1+ r) ^t))
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| Perpetuities & Annuities | Applications
Value of payments
Implied interest rate for an annuity
Calculation of periodic payments
Mortgage payment
Annual income from an investment payout
Future Value of annual payments
FV = C [(1/r) - (1/(r (1+ r) ^t)) X (1 + r
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| Effective Annual Interest Rate | Effective Annual Interest Rate - Interest rate that is annualized using compound interest (i.e. the rate a which invested funds grow over the course of a year).
1 + EAR =〖( 1+ monthly rate)〗_12
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| Annual Percentage Rate | Annual Percentage Rate - Interest rate that is annualized using simple interest.
APR = Monthly rate x 12
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| Inflation | Inflation - Rate at which prices as a whole are increasing.
Remember: Current dollar cash flows must be discounted by the nominal interest rate; real cash flows must be discounted by the real interest rate.
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| Nominal interest rate | Nominal Interest Rate - Rate at which money invested grows.
1 + real interest rate = (1 + nominal interest rate)/(1+ inflation rate)
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| Real interest rate | Real Interest Rate - Rate at which the purchasing power of an investment increases.
Real interest rate ≈ nominal int. rate – inflation rate
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